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correlate the values found When transposed les are used for statistical purposes, the updating or re-creation of the transposed le may be done only periodically This process is analogous to a le reorganization The potentially very long records, R = nV for one attribute, can easily exceed the limits of available analysis programs in terms of storage space The processing time required for such long records also will become more signi cant The analysis of very large quantities of data will also require consideration of the numerical stability or accuracy of the analysis algorithm used The assumption made in most other examples that the computational time can be neglected is not valid when processing records from transposed les A record of a transposed le shows much similarity with the lowest level of an exhaustive index A transposed le, however, stands more on its own; it does not need to contain pointers from the transposed le to the main le It may be convenient to use a transposed le as input to a program which generates indexes to the main le If the record positions of the main le cannot be computed, the transposed le can contain one record with values of all the original source record positions
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Transposition of a File The e ort needed to transpose a large le with many attributes is large The most obvious procedure is to construct one transposed record during one exhaustive read of the le To transpose all of a le in this manner will require a time equal to a TX for the a passes over the le If blocks for multiple transposed records (buf ) can be built up in core at a time, only a/buf passes over the le are required Floyd74 describes two transposition algorithms which take on the order of log2 w passes where w is the greater of n or a The simpler algorithm generates records increasing gradually in size to n; the second algorithm is given as Example 4-1 and generates each transposed record as a sequence of pieces of size a and requires only three bu ers of that size
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Transposition Program The program shown as Example 4-1 on pages 176 and 177 transposes a source le using n/a (2+ log2 a )a fetches and as many insertions Most of the operations are not sequential and will require a seek The bene t of this procedure will become substantial when a/buf 10
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/* Program to transpose a source file of 'n'records of length 'a' The input and output files are sequential The program contains three distinct sections: 1 Copy groups of 'a'records to a work file, resequencing all but the first record of a group in inverse order Values in these records are circularly shifted so that the first column elements form a diagonal The last group is padded with zeroes 2 Record pairs within groups are selected, and within each pair alternate entries are transferred to rotate columns by 1,2,4,8, using powers of two in log2(a) passes per group 3 When all groups are rearranged, the work file is copied, shifting each record to the final postion, to the output file */ file transpose: PROCEDURE(source,transposed,n,a); DECLARE(source,transposed,work) FILE; DECLARE(spacein,spaceout,save)(a); DEFAULT RANGE(*) FIXED BINARY; DECLARE(MOD,MIN)BUILTIN; /* The transposition proceeds in groups of "a" records */ groups = (n-1)/a+1; amin1 = a-1; record in = 0; /* Perform sections 1 and 2 for each group and leave re- */ /* sults on the work file */ g loop: DO group = 1 TO groups; /* Copy and rearrange a group for permutation */ loop 1: DO out rec pos = a TO 1 BY -1; IF record in<n THEN READ FILE(source) INTO(spacein); ELSE spacein = 0; record in = record in+1; base out = a*(group-1)+1; /* Shift records to align columns so that transposition can proceed in parallel blocks */ CALL movearound(out rec pos); record out = MOD(out rec pos, a) + base out; WRITE FILE(work) KEYFROM(record out) FROM(spaceout); END loop 1; /* Set up number of passes to permute one group */ order = 1; order2 = 2; loop 2: DO WHILE( order<a ); /* Permute records by order = 1,2,4,8, */ CALL rearrange(base out); order = order2; order2 = order*2; END loop 2; END g loop; /* Now copy the result from each transposed group to the */ loop 3: DO shift = 0 TO amin1; /* output file */ /* Each record contains "groups" segments of length "a"*/ a loop: DO rec = shift+1 BY a TO base out-1; READ FILE(work) KEY(rec) INTO(spacein); CALL movearound(shift); WRITE FILE(transposed) FROM(spaceout); END a loop; END loop 3;
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